On the Analysis of the Discrete-Time Geom(n)/G(n)/1/N Queue

Abstract

In this paper, we discuss the late-arrival discrete-time Geom(n)/G(n)/1/N queue with state-dependent arrival and service processes. Whereas the interarrival times are geometrically distributed, service times are conditioned on the system length at the moment of service initiation. The model has wide applications in computer-communications systems, broadband integrated service digital network, asynchronous transfer mode, and so on. The analysis of the model has been carried out, using the supplementary variable technique, and the final results are presented in the form of recursive equations that can be easily implemented on any personal computer. In addition, relations among state probabilities at prearrival, postdeparture, and random epochs have been developed. To demonstrate the effectiveness of our method, some numerical examples have been presented for service-time distributions such as geometric, deterministic, arbitrary, and mixed. The results obtained in this paper should be found useful by system designers who wish to control the congestion by adjusting the service rate if the arrival traffic changes.